In this article, we consider a dual-hop full-duplex (FD), amplify-and-forward, orthogonal frequency division multiplexing (OFDM) relaying network, where the relay operates based on a time-switching architecture to harvest energy from radio frequency signals. We use a polarization-enabled digital self-interference cancellation (PDC) scheme to cancel the self-interference signal at the relay in order to achieve FD communications. The paper provides a comprehensive analysis of the system performances in terms of outage probability and throughput over multipath Rayleigh fading channels. Furthermore, the optimal time split between the duration of energy harvesting and signal transmission to maximize the system throughput is numerically calculated. We also derive the asymptotic lines to simplify the expressions of outage probability and throughput at high transmit signal-to-noise ratios (SNR). Our analysis and simulation results show that the proposed FD relaying system by utilizing a proper time split fraction can boost the system throughput significantly over an appreciable range of transmitting SNR values, compared to half-duplex (HD) relaying systems.